PS3 (9-11)- 8 Students demonstrate an understanding of forces and motion by…
8a predicting and/or graphing the path of an object in different reference planes and explain how and why (forces) it occurs.
8b using modeling, illustrating, graphing explain how distance and velocity change over time for a free falling object.
National Standards:
Context of Lesson:
One of the biggest problems facing an instructor of physics is in trying to help students blast through surface understanding of the concepts and to obtain true understanding of the material. This particular lesson is a case in point. If you go to any student in any physics class in the country and ask them 'what is the difference between speed and velocity?' Guaranteed the students will respond with 'Velocity is speed and direction.' Yet if you put a displacement vs time graph in front of them with a line going diagonally down across the page a large percentage of those students would say 'the object is slowing down.' This is because there is a disconnect between the student understanding the definition of velocity and being able to apply it to a graphical representation of that concept. With this in mind Day 2 and Day 3 of this unit are devoted to establishing a firm grounding in graphical representations of position vs time and then using these graphs as a spring board into a discussion of why the concept of velocity is necessary for our understanding of motion.
Opportunities to Learn:
Students will be given the opportunity to work in pairs to collect data. The groups will then combine their data and construct a 'distance' vs 'time' graph (and a 'time' vs 'distance' graph). Students will use a best line fit to determine the slope of the line and then discuss what the slope of this line tells us about the motion (speed). Students will then create a speed vs time graph using those slopes. Students will then be given an opportunity to apply the patterns that they see in the graphs to a variety of different graphs and to predict what the graphs would look like in various scenarios (no accelerations though).
Depth of Knowledge
DOK 3 a - Interpret information from a complex graph (such as determining features of the graph or aggregating data in the graph)
Prerequisite Knowledge
Students will only be required to have a basic understanding of speed and graphing
Plans for Differentiating Instruction
Exceeds Proficiency: students will be challenged to predict what the graph would look like for an object that is increasing its speed or decreasing its speed. Students will be asked to look for possible errors and improvements.
Approaching Proficiency: Instructor will move around the classroom making sure that students are confident in graphing (as most are)
Accommodations and modifications
Environmental factors
Materials
stopwatches
graphing paper
rulers
Objectives:
Students will be able to construct a 'distance' vs 'time' graph from a data table
Students will be able to calculate the 'speed' of an object using the slope from a 'distance' vs 'time' graph
Students will be able to construct a 'speed' vs 'time' graph using the calculated values of slope
Students will be able to explain why we use 'distance' vs 'time' graphs instead of 'time' vs 'distance' graphs
Students will be able to predict the graphs from a scenario and create a scenario from a graph
Instruction:
Opening:
Students will be greeted by instructor and handed a green pen and answer sheet. Students will be instructed to pull out their homework and quickly correct their answer sheet using the green pen (It is important to explain to the students that they will not be penalized for having a lot of green ink, they will be penalized for not honestly attempting their homework or not self correcting. Students that use 'non-green' ink will receive a zero for their homework as this is cheating). Students will only be given 5 mins to check their answers while teacher takes attendance and check homework for completion. Teacher will collect all answer sheets
Engagement:
Instructor will put a bunch of number sets (different intervals for an x^2 + 3 function)on the board at random and ask the students what the pattern is. Students will have difficulty. Instructor will then arrange the sets in order and ask the students what the pattern is. Perhaps one student will be able to see the pattern. Then put a graph of the sets on the board. All of the students will see the pattern (might not be able to call it a 'power function' but they will all recognize that there is a pattern). Instructor will then give the students a few minutes to explain (or written reflection) as to why we make graphs of data and then the instructor uses this discussion as a springboard into the question "I wonder what a graph of motion would show us?"
Instructor will explain that the class will be going out into the hall and record the time as 'someone' runs down the hall. Explain that there are numbers marked on the wall at even intervals down the hall and each group is to stand at one of these numbers and record the time it takes for that 'someone' to cross infront of them. There will be 3 trials: Walk, Jog, and Sprint. Instructor will ask for a volunteer (most likely there will not be one, unless there is a student on the track team) If no one volunteers then the instructor will do it (ham it up, pull out a gym bag and put on some running shoes and a sweat band). Students will record their group number and the times
Students will return to class and put their data up on the board. Students will then make one graph with all 3 sets of data on it (remind students to label their plots). The stopwatch partner will do a x vs t graph while the recorder will do a t vs x graph. The instructor will walk around and talk to students (I see that you are using lines to connect the data points, what do these zig zag lines tell you about a pattern? Is there a better way?)
Students will compare their graphs with their partner and come up with an explanation as to why they look different (slope of x vs t = 'speed' while slope of t vs x = 'slowness')
Instructor will lead a discussion as to why we do x vs t and what the slope tells us (talk about units too)
Students will create a best fit line for each data set and then calculate the speed by calculating the slope.
Instructor will ask the groups to calculate the speed for different time intervals on the graph (the slope will be the same and therefore the speed is the same)
Instructor will ask what a 'speed' vs time graph would look like (straight horizontal line, y = speed)
Instructor will then pass out worksheet and walk around classroom
Closure:
Students will be reminded about the day's question 'Why do we graph?' and will be asked to take a minute to reflect about the days lesson and answer that question.
Instructor will get a strong idea of students performance by walking around the room and observing how they construct their graphs furthermore the reflection sheet will allow the instructor to see if they can verbalize what they have learned.
Lesson Plan
Lesson Title: Why do we graph?
State Standards: GLEs/GSEs
PS3 (9-11)- 8Students demonstrate an understanding of forces and motion by…
National Standards:
Context of Lesson:
One of the biggest problems facing an instructor of physics is in trying to help students blast through surface understanding of the concepts and to obtain true understanding of the material. This particular lesson is a case in point. If you go to any student in any physics class in the country and ask them 'what is the difference between speed and velocity?' Guaranteed the students will respond with 'Velocity is speed and direction.' Yet if you put a displacement vs time graph in front of them with a line going diagonally down across the page a large percentage of those students would say 'the object is slowing down.' This is because there is a disconnect between the student understanding the definition of velocity and being able to apply it to a graphical representation of that concept. With this in mind Day 2 and Day 3 of this unit are devoted to establishing a firm grounding in graphical representations of position vs time and then using these graphs as a spring board into a discussion of why the concept of velocity is necessary for our understanding of motion.Opportunities to Learn:
Students will be given the opportunity to work in pairs to collect data. The groups will then combine their data and construct a 'distance' vs 'time' graph (and a 'time' vs 'distance' graph). Students will use a best line fit to determine the slope of the line and then discuss what the slope of this line tells us about the motion (speed). Students will then create a speed vs time graph using those slopes. Students will then be given an opportunity to apply the patterns that they see in the graphs to a variety of different graphs and to predict what the graphs would look like in various scenarios (no accelerations though).Depth of Knowledge
DOK 3 a - Interpret information from a complex graph (such as determining features of the graph or aggregating data in the graph)Prerequisite Knowledge
Students will only be required to have a basic understanding of speed and graphingPlans for Differentiating Instruction
Exceeds Proficiency: students will be challenged to predict what the graph would look like for an object that is increasing its speed or decreasing its speed. Students will be asked to look for possible errors and improvements.Approaching Proficiency: Instructor will move around the classroom making sure that students are confident in graphing (as most are)
Accommodations and modifications
Environmental factors
Materials
stopwatchesgraphing paper
rulers
Objectives:
Instruction:
Opening:
Students will be greeted by instructor and handed a green pen and answer sheet. Students will be instructed to pull out their homework and quickly correct their answer sheet using the green pen (It is important to explain to the students that they will not be penalized for having a lot of green ink, they will be penalized for not honestly attempting their homework or not self correcting. Students that use 'non-green' ink will receive a zero for their homework as this is cheating). Students will only be given 5 mins to check their answers while teacher takes attendance and check homework for completion. Teacher will collect all answer sheetsEngagement:
Instructor will put a bunch of number sets (different intervals for an x^2 + 3 function)on the board at random and ask the students what the pattern is. Students will have difficulty. Instructor will then arrange the sets in order and ask the students what the pattern is. Perhaps one student will be able to see the pattern. Then put a graph of the sets on the board. All of the students will see the pattern (might not be able to call it a 'power function' but they will all recognize that there is a pattern). Instructor will then give the students a few minutes to explain (or written reflection) as to why we make graphs of data and then the instructor uses this discussion as a springboard into the question "I wonder what a graph of motion would show us?"Instructor will explain that the class will be going out into the hall and record the time as 'someone' runs down the hall. Explain that there are numbers marked on the wall at even intervals down the hall and each group is to stand at one of these numbers and record the time it takes for that 'someone' to cross infront of them. There will be 3 trials: Walk, Jog, and Sprint. Instructor will ask for a volunteer (most likely there will not be one, unless there is a student on the track team) If no one volunteers then the instructor will do it (ham it up, pull out a gym bag and put on some running shoes and a sweat band). Students will record their group number and the times
Students will return to class and put their data up on the board. Students will then make one graph with all 3 sets of data on it (remind students to label their plots). The stopwatch partner will do a x vs t graph while the recorder will do a t vs x graph. The instructor will walk around and talk to students (I see that you are using lines to connect the data points, what do these zig zag lines tell you about a pattern? Is there a better way?)
Students will compare their graphs with their partner and come up with an explanation as to why they look different (slope of x vs t = 'speed' while slope of t vs x = 'slowness')
Instructor will lead a discussion as to why we do x vs t and what the slope tells us (talk about units too)
Students will create a best fit line for each data set and then calculate the speed by calculating the slope.
Instructor will ask the groups to calculate the speed for different time intervals on the graph (the slope will be the same and therefore the speed is the same)
Instructor will ask what a 'speed' vs time graph would look like (straight horizontal line, y = speed)
Instructor will then pass out worksheet and walk around classroom
Closure:
Students will be reminded about the day's question 'Why do we graph?' and will be asked to take a minute to reflect about the days lesson and answer that question.Instructor will pass out homework
Assessment:
Instructor will get a strong idea of students performance by walking around the room and observing how they construct their graphs furthermore the reflection sheet will allow the instructor to see if they can verbalize what they have learned.Homework will be self corrected the following day
Reflections
(only done after lesson is enacted)Student Work Sample 1 – Approaching Proficiency:
Student Work Sample 2 – Proficient:
Student Work Sample 3 – Exceeds Proficiency: